Linda J S Allen

Summary

Affiliation: Texas Tech University
Country: USA

Publications

  1. ncbi request reprint Stochastic epidemic models with a backward bifurcation
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042
    Math Biosci Eng 3:445-58. 2006
  2. doi request reprint Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models
    L J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, United States Electronic address
    Math Biosci 243:99-108. 2013
  3. ncbi request reprint Mathematical models for hantavirus infection in rodents
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409 1042, United States of America
    Bull Math Biol 68:511-24. 2006
  4. pmc A habitat-based model for the spread of hantavirus between reservoir and spillover species
    Linda J S Allen
    Texas Tech University, Department of Mathematics and Statistics, Lubbock, TX 79409, USA
    J Theor Biol 260:510-22. 2009
  5. doi request reprint Stochastic models for competing species with a shared pathogen
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, United States
    Math Biosci Eng 9:461-85. 2012
  6. ncbi request reprint Disease emergence in multi-host epidemic models
    Robert K McCormack
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Math Med Biol 24:17-34. 2007
  7. ncbi request reprint A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability
    Edward J Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Math Biosci 196:14-38. 2005
  8. ncbi request reprint Genetic models for plant pathosystems
    Jacob C Kesinger
    Department of Mathematics and Statistics, Texas Tech University, P O Box 41042, Lubbock, TX 79409 1042, USA
    Math Biosci 177:247-69. 2002
  9. pmc Stochastic models for virus and immune system dynamics
    Yuan Yuan
    Department of Mathematics, Texas Tech University, Lubbock, TX 79409, USA
    Math Biosci 234:84-94. 2011
  10. ncbi request reprint Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission
    Chandrani Banerjee
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Math Biosci Eng 5:617-45. 2008

Collaborators

Detail Information

Publications22

  1. ncbi request reprint Stochastic epidemic models with a backward bifurcation
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042
    Math Biosci Eng 3:445-58. 2006
    ..For population sizes N=/>1000, the deterministic and stochastic models agree, but for small population sizes the stochastic models indicate that the backward bifurcation may have little effect on the disease dynamics...
  2. doi request reprint Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models
    L J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, United States Electronic address
    Math Biosci 243:99-108. 2013
    ..These relations are illustrated, analytically and numerically, in two settings, a general stage-structured model and a vector-host model applied to West Nile virus in mosquitoes and birds...
  3. ncbi request reprint Mathematical models for hantavirus infection in rodents
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409 1042, United States of America
    Bull Math Biol 68:511-24. 2006
    ..These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels...
  4. pmc A habitat-based model for the spread of hantavirus between reservoir and spillover species
    Linda J S Allen
    Texas Tech University, Department of Mathematics and Statistics, Lubbock, TX 79409, USA
    J Theor Biol 260:510-22. 2009
    ..Environmental changes that result in greater habitat overlap result in more encounters among various species that may lead to pathogen outbreaks and pathogen establishment in a new host...
  5. doi request reprint Stochastic models for competing species with a shared pathogen
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, United States
    Math Biosci Eng 9:461-85. 2012
    ..Finally, numerical simulations are conducted to explore the effect of disease on two-species competition, to illustrate some of the analytical results and to highlight some of the differences in the stochastic and deterministic models...
  6. ncbi request reprint Disease emergence in multi-host epidemic models
    Robert K McCormack
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Math Med Biol 24:17-34. 2007
    ..Numerical examples illustrate the dynamics of the two- and three-host epidemic models. The models have applications to hantavirus in rodents and other zoonotic diseases with multiple hosts...
  7. ncbi request reprint A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability
    Edward J Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Math Biosci 196:14-38. 2005
    ....
  8. ncbi request reprint Genetic models for plant pathosystems
    Jacob C Kesinger
    Department of Mathematics and Statistics, Texas Tech University, P O Box 41042, Lubbock, TX 79409 1042, USA
    Math Biosci 177:247-69. 2002
    ..The original model of Leonard has this same property. However, with random selection values, solutions tend to converge toward the polymorphic equilibrium...
  9. pmc Stochastic models for virus and immune system dynamics
    Yuan Yuan
    Department of Mathematics, Texas Tech University, Lubbock, TX 79409, USA
    Math Biosci 234:84-94. 2011
    ..It is shown that the probability of a successful invasion depends on the initial viral dose, whether the immune system is activated, and whether the release strategy is bursting or budding...
  10. ncbi request reprint Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission
    Chandrani Banerjee
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Math Biosci Eng 5:617-45. 2008
    ..Numerical examples illustrate the dynamics of the models. The biological implications of the results and future research goals are discussed in the conclusion...
  11. pmc Stochastic model of an influenza epidemic with drug resistance
    Yaji Xu
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    J Theor Biol 248:179-93. 2007
    ..Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated...
  12. doi request reprint Basic stochastic models for viral infection within a host
    Sukhitha W Vidurupola
    Texas Tech University, Department of Mathematics and Statistics, Lubbock, Texas 79409 1042, United States
    Math Biosci Eng 9:915-35. 2012
    ..In addition, the SDE models show significant variability in the timing of the viral peak. The viral peak is earlier for viruses that are released from infected cells via bursting rather than via budding from the cell membrane...
  13. doi request reprint Stability and permanence in gender- and stage-structured models for the boreal toad
    D K Mallawaarachchi
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    J Biol Dyn 5:1-26. 2011
    ..If ℛ(0)>1 and ℛ(F)<1, then the population becomes disease-free. However, if both thresholds are greater than one, the population levels are severely reduced by the fungal pathogen...
  14. doi request reprint Extinction thresholds in deterministic and stochastic epidemic models
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    J Biol Dyn 6:590-611. 2012
    ..In this investigation, we summarize some of the deterministic and stochastic threshold theory, illustrate how to calculate the stochastic thresholds, and derive some new relationships between the deterministic and stochastic thresholds...
  15. doi request reprint The basic reproduction number in epidemic models with periodic demographics
    Curtis L Wesley
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA
    J Biol Dyn 3:116-29. 2009
    ..The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains...
  16. ncbi request reprint The dynamics of two viral infections in a single host population with applications to hantavirus
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Math Biosci 186:191-217. 2003
    ..It is shown through analysis and numerical simulations that both diseases can be maintained within a single host population, where individuals can be either infected with both viruses or with a single virus...
  17. ncbi request reprint A comparison of three different stochastic population models with regard to persistence time
    Linda J S Allen
    Department of Mathematics and Statistics, Texas Tech University, MS 1042, 117I, Lubbock, TX 79409 1042, USA
    Theor Popul Biol 64:439-49. 2003
    ..Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth...
  18. doi request reprint Probability of a disease outbreak in stochastic multipatch epidemic models
    Glenn E Lahodny
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Bull Math Biol 75:1157-80. 2013
    ....
  19. ncbi request reprint Coexistence of multiple pathogen strains in stochastic epidemic models with density-dependent mortality
    Nadarajah Kirupaharan
    Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409 1042, USA
    Bull Math Biol 66:841-64. 2004
    ..The initial number of infected individuals, the basic reproduction numbers, and other epidemiological parameters are important determinants of the dominant strain in the stochastic epidemic model...
  20. ncbi request reprint A spatially structured metapopulation model with patch dynamics
    Dashun Xu
    Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
    J Theor Biol 239:469-81. 2006
    ..We also derive a stochastic differential equations (SDE) model of the Itô type based on our deterministic model. Our simulations reveal good agreement between the deterministic model and the SDE model...
  21. ncbi request reprint Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size
    Azmy S Ackleh
    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504 1010, USA
    J Math Biol 47:153-68. 2003
    ..In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur...
  22. ncbi request reprint Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion
    Azmy S Ackleh
    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504 1010, USA
    Theor Popul Biol 71:290-300. 2007
    ..Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded...